A short precis: endurance running provided access to a high protein diet, altering human body shape and the human brain over generations.

This change is assumed to be due to increased neurotrophin levels. These levels are increased with this kind of exercise in mammals and humans. In turn the elevated neurotrophin stimulates brain function. There is a literature review supporting this position.

.... exercise and/or training would result in a higher BDNF synthesis following an acute exercise bout (i.e. compared with untrained subjects). Subsequently, more BDNF could be released into the blood circulation which may, in turn, be absorbed more efficiently by central and/or peripheral tissues where it could induce a cascade of neurotrophic and neuroprotective effects.

I take the results in those reviews as saying 'Yes, there is a cognitive benefit to long term exercise (being in shape), and particulary after long distance running'.

In modern non-scientific jargon: 'Exercise increases your ability rewire your brain' - learn and retain wholly new tasks. If you use this to benefit your 'Halo' game or learn a new programming language - it is all up to you.

But... You could interpret that as being more susceptible to propaganda or just having more neurons.

I would want to see that the specific neural changes actually produce a cognitive benefit in controlled behavioral tests.

Mostly because neural systems are highly degenerate. (See Eve Marders work). Several different neural configurations (in terms if parameters like connection strength and potassium conductance) can lead to the same functional result.

Proposed models like these are meant to be a synthesis of existing knowledge as an approach to understanding something new.

IMO, proposing ways in which to expand or correct or even invalidate the model using your criticism is great. Simply dismissing a model on the basis as the 'same old same old' isn't very enlightened. Or useful, IMO. It obviates being published in the first place.

If you want to completely negate it, that's great, but a little contrapunctus is in order, i.e., cite some work that negates the hypothesis. The paper I cited originally (saw a pre-print) will be out Jan 13. I think. I assume it won't be all that changed. Go from there. BTW you're gonna have a lot citing to do. My opinion only. YMMV.

N.B.: neurophyisiology is not my strong point. I was a population biologist years and years ago. Now I twiddle bits and invert bytes.

It doesn't seem as if the article is proposing that training for a marathon will considerably improve your brain functions. I, of course, can't say this for certain, because I'm only able to read the Abstract right now.

What it does say, however, is this:

We review evidence that selection acting on endurance increased baseline neurotrophin and growth factor signalling (compounds responsible for both brain growth and for metabolic regulation during exercise) in some mammals, which in turn led to increased overall brain growth and development. This hypothesis suggests that a significant portion of human neurobiology evolved due to selection acting on features unrelated to cognitive performance.

Click to expand...

That clearly states that the act of partaking in long endurance running affected (notice the past tense used here, and in the article when stating "evolved"), and increased, the general functions of our brains during our evolution. As I'm sure you know, evolution doesn't happen to one single individual over the course of their lifetime. This is merely stating that there is evidence suggesting that long endurance running affected how our brains evolved. It's not saying that running will immediately alter our cognitive abilities.

To me, the article seems interesting because our increase in brain size appears to merely be a byproduct of an increase in stamina, and that humans with better stamina had more access to food, and thus, following natural selection, humans with better stamina passed on their genes rather than people with worse stamina, who also, as a consequence of their lack of endurance, had a less noticeable growth in their brain functions.

This is made apparent by the statement, "This hypothesis suggests that a significant portion of human neurobiology evolved due to selection acting on features unrelated to cognitive performance."

Maybe our larger brains weren't viewed as highly in evolution as we once thought, and our physical abilities took precedence? Interesting stuff.

EDIT: I suppose a more direct answer to your original question would be that the brain simply grew. From what the Abstract states, no individual cognitive performance benefited solely, but all processes increased as a whole.